On the Tuning of Predictive Controllers:  Inverse Optimality and the Minimum Variance Covariance Constrained Control Problem

Abstract

This paper presents a systematic tuning approach for linear model predictive controllers based on the computationally attractive minimum variance covariance constrained control (MVC 3 ) problem. Unfortunately, the linear feedback policy generated by the MVC 3 problem is incompatible with the algorithmic framework of predictive control, in which the primary tuning vehicle is the selection of objective function weights. The main result of this paper is to show that all linear feedbacks generated by the MVC 3 problem exhibit the property of inverse optimality with respect to an appropriately defined linear quadratic regulator (LQR) problem. Thus, the proposed tuning scheme is a two-step procedure: application of the MVC 3 problem to achieve tuning objectives, followed by application of inverse optimality to determine the predictive control weights from the MVC 3 -generated linear feedback.

Inventory control and LQG: Connections and extensions

“…The constrained minimum variance (CMV) control problem, defined in Chmielewski & Manthanwar (2004) is:…”

“…In Chmielewski and Manthanwar (2004), it is shown that all controllers generated by the CMV problem are equal to some LQG controller.…”

On the tuning of predictive controllers: Application of generalized Benders decomposition to the ELOC problem

“…In the first installment (Chmielewski and Manthanwar, 2004) of this series on the tuning of predictive controllers, (Chmielewski and Manthanwar, 2004;Omell and Chmielewski, 2014) it was shown that the linear feedback generated by the minimum variance covariance constrained control (MVC 3 ) problem is guaranteed to be in the family of Linear Quadratic Regulator (LQR) feedback policies. In addition, using the inverse optimality results of Chmielewski and Manthanwar (2004), one could generate quadratic objective function weights such that if used within the LQR problem, the resulting controller would be identical to the MVC 3 policy.…”

“…In addition, using the inverse optimality results of Chmielewski and Manthanwar (2004), one could generate quadratic objective function weights such that if used within the LQR problem, the resulting controller would be identical to the MVC 3 policy. It was then postulated that such a scheme could be used within a predictive controller context to tune the controller (i.e., select quadratic objective function weights) such that the weights and the point-wise-in-time constraints would be in alignment.…”

“…Thus, a more descriptive name for the MBOP problem is the economic linear optimal control (ELOC) problem, which will generate a linear feedback policy termed the ELOC policy. Given the ELOC policy, one can again use the inverse optimality results of Chmielewski and Manthanwar (2004) to generate a predictive form of the ELOC policy. If one then imposes point-wise-in-time constraints to the (unconstrained) predictive form of the ELOC, the resulting controller is denoted as the constrained ELOC policy.…”